Generation of multiple-vortex beams in the process of diffraction of cosine-Laguerre-Gaussian laser beam by the fork-shaped grating

We present the theoretical study about Fraunhofer diffraction of cosine-Laguerre-Gaussian laser beam of mode (1, n = 0) by the fork-shaped grating with a phase singularity of integer order p. The analytical expressions for the diffracted wave field amplitude and intensity distributions are derived. The transverse intensity and phase profiles of the diffracted beam, in a given diffraction order and for different values of l and p, are calculated. They show that the higher diffraction orders are multiple-vortex beams. In addition, the interference patterns of the diffracted wave field with a slightly inclined plane wave are presented, for confirming the presence of the optical vortices and determining the values and signs of their topological charges. We have shown how an azimuthally shaped, non-vortex beam, consisting of 2l bright lattices, can be transformed into a fan of multiple-vortex beams in the higher diffraction orders.